Legendre-Gauss Quadrature Points

The related theory is well presented by [weisstein].

Code to generate points

The following Mathematica script, taken from [pomax] was used to generate the Legendre-Gauss quadrature points:

symboliclegendre[n_,x_]:=Solve[LegendreP[n,x]==0];
legendreprime[n_,a_]:=D[LegendreP[n,x],x]/.x->a;
weights[n_,x_]:=2/((1-x^2) legendreprime[n,x]^2);

(*how many terms should be generated*)
h=64;

(*what numerical precision is desired?*)
precision=54;

str=OpenWrite["out_legendre_gauss_quadrature_points.txt"];
Do[Write[str];Write[str,"n = "<>ToString[n]];
nlist=symboliclegendre[n,x];
xnlist=x/.nlist;
Do[Write[str,FortranForm[Re[N[Part[xnlist,i],precision]]]],{i,Length[xnlist]}];,{n,2,h}];
Close[str];
str=OpenWrite["out_legendre_gauss_quadrature_weights.txt"];
Do[Write[str];Write[str,"n = "<>ToString[n]];
slist:=symboliclegendre[n,x];
xslist=x/.slist;
Do[Write[str,FortranForm[Re[N[weights[n,Part[xslist,i]],precision]]]],{i,Length[xslist]}];,{n,2,h}];
Close[str];

points.txt

The points are listed below:

weights.txt

The weights are listed below: